Question

Giải PT:

\(\dfrac{1}{2}sin\left(x+10^o\right)-\dfrac{\sqrt{3}}{2}sin\left(80^o-x\right)=cos3x\)

Answer 1

\(\Leftrightarrow\dfrac{1}{2}\sin\left(x+10^0\right)-\dfrac{\sqrt{3}}{2}\cdot\cos\left(x+10^0\right)=\cos3x\)

\(\Leftrightarrow\sin\left(x+10^0-60^0\right)=\sin\left(90^0-3x\right)\)

\(\Leftrightarrow\sin\left(x-50^0\right)=\sin\left(90^0-3x\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x-50^0=90^0-3x+k\cdot360^0\\x-50^0=180^0-90^0+3x+k\cdot360^0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}4x=140^0+k\cdot360^0\\-2x=140^0+k\cdot360^0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=35^0+k\cdot90^0\\x=-70^0-k\cdot180^0\end{matrix}\right.\)